{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=10000\n",
    "m=100\n",
    "p=3 #Barabasi-Albert parameter\n",
    "init_Theta=0.01 #0.06\n",
    "N=100 #number of time steps\n",
    "r=1 #0.3 #szansa aktywacji przy negatywnej korelacji\n",
    "prob=0.20 #prawd. aktywności użytkownika w danej epidemii (do generaowania macierzy)\n",
    "a=0.02 # parameter kształtu powr-law"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.Undirected graph done!\n",
      "2.Directed graph done!\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2d615d99a162466cb2ab271a35ce5e51",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=59982), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "3.Wieghts assigned!\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1123977b6fbc4d17be97cd92f3b3b50d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=10000), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "4.Wieghts normalized!\n",
      "4.Adjacency (sparse) matrix created!\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "np.set_printoptions(threshold=np.nan)\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "import networkx as nx\n",
    "import scipy.sparse as sparse\n",
    "import asizeof\n",
    "G=nx.barabasi_albert_graph(n, p)\n",
    "print('1.Undirected graph done!')\n",
    "G=G.to_directed()\n",
    "print('2.Directed graph done!')\n",
    "for u,v in tqdm(G.edges()):\n",
    "    G[u][v]['weight']=1.0#np.random.uniform(0,1)\n",
    "print('3.Wieghts assigned!')\n",
    "for i in tqdm(range(n)):\n",
    "    in_degree=G.in_degree(i,weight='weight')\n",
    "    for u,v in G.in_edges(i):\n",
    "        #print(u,v,G[u][v]['weight'],G[u][v]['weight'] / in_degree, in_degree)\n",
    "        G[u][v]['weight']/=in_degree\n",
    "print('4.Wieghts normalized!')\n",
    "W=nx.adjacency_matrix(G,weight='weight')\n",
    "print('4.Adjacency (sparse) matrix created!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.99935432344 1.0 0.017621881058 0.0253369137813\n"
     ]
    }
   ],
   "source": [
    "C = np.random.random((m, m))\n",
    "C=C*2-1\n",
    "C *= np.tri(*C.shape,k=-1)\n",
    "C=C+np.transpose(C)+np.eye(m)\n",
    "print(C.min(),C.max(),C.mean(),np.median(C))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61068905277670815"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C[23][45]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "# indykatory=[]\n",
    "# frakcje=[]\n",
    "# I=np.random.choice(a=[False,True], size=(n,m), replace=True, p=[1-prob, prob])\n",
    "# I=I.reshape((1, n*m))\n",
    "# I=np.random.permutation(I).reshape((n,m))\n",
    "# indykatory.append(I)\n",
    "# frakcje.append(np.vstack((range(m),np.sum(I,axis=0)/n)))\n",
    "# I=I.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4e58fca6ff184ea38af68c4cf8349456",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "indykatory=[]\n",
    "frakcje=[]\n",
    "import scipy.stats as stats\n",
    "frac_inf=np.ceil(stats.powerlaw.rvs(a,size=(m))*n).astype(int)\n",
    "I=np.full((n, m), False, dtype=bool)\n",
    "for i in tqdm(range(m)):\n",
    "    I[np.ix_(stats.randint.rvs(0, n-1, size=frac_inf[i]),[i])]=True\n",
    "indykatory.append(I)\n",
    "frakcje.append(np.vstack((range(m),np.sum(I,axis=0)/n)))\n",
    "I=I.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "# frac_inf.mean()/n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "# x = np.linspace(stats.powerlaw.ppf(0.01, a),\n",
    "# ...                 stats.powerlaw.ppf(0.99, a), 100)\n",
    "# plt.plot(x, stats.powerlaw.pdf(x, a),\n",
    "# ...        'r-', lw=5, alpha=0.6, label='powerlaw pdf')\n",
    "# plt.show()\n",
    "# mean, var, skew, kurt = stats.powerlaw.stats(a, moments='mvsk')\n",
    "# print(mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8828b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([  1.00000000e-04,   2.41700000e-01,   3.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.23000000e-02,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.45000000e-02,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         5.00000000e-04,   1.00000000e-04,   2.70000000e-03,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   3.30000000e-02,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.38200000e-01,\n",
       "         1.00000000e-04,   4.99000000e-02,   1.35000000e-02,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   5.88000000e-02,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         4.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         2.56800000e-01,   5.50000000e-03,   1.00000000e-04,\n",
       "         4.99600000e-01,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   3.49000000e-02,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04,   1.00000000e-04,   1.00000000e-04,\n",
       "         1.00000000e-04])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.plot(frakcje[0][1], 'ro')\n",
    "axes = plt.gca()\n",
    "axes.set_ylim([0,1])\n",
    "plt.show()\n",
    "frakcje[0][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.array_equal(I_int,I_prim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.array_equal(np.where(np.greater_equal(W.transpose().dot(I_int).dot(C)/m,Theta)==True)[0],np.where(np.greater_equal(W.transpose().dot(I_prim).dot(C)/m,Theta)==True)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "Theta=np.full((n,m), init_Theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y=np.full((n,1),0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "#F.max()\n",
    "#F[np.ix_(list(range(0,7)),list(range(0, 7)))]\n",
    "#F.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 100)"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "#U[np.ix_(np.nonzero(I[:,[23]] * I[:,[45]])[0],[23,45])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([], shape=(0, 2), dtype=bool)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I[np.ix_(np.nonzero(I[:,[23]] * I[:,[45]])[0],[23,45])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ea7e40c433cd450b9f7c6f17bca3debc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "HBox(children=(IntProgress(value=0), HTML(value='')))"
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     },
     "metadata": {},
     "output_type": "display_data"
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     "name": "stdout",
     "output_type": "stream",
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      "-0.0966857504521 0.166930378615 0.0192901452478 82\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 83\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 84\n",
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      "-0.0966857504521 0.166930378615 0.0192901452478 86\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 87\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 88\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 89\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 90\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 91\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 92\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 93\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 94\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 95\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 96\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 97\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 98\n",
      "-0.0966857504521 0.166930378615 0.0192901452478 99\n",
      "\n"
     ]
    }
   ],
   "source": [
    "cor_23_45=np.empty([0,2])\n",
    "for l in tqdm(range(N)):    \n",
    "    U=W.transpose().dot(I)\n",
    "    #cor_23_45=np.concatenate((cor_23_45, U[np.ix_(np.nonzero(I[:,[23]] * I[:,[45]])[0],[23,45])]), axis=0)\n",
    "    cor_23_45=np.concatenate((cor_23_45, U[:,[23,45]]), axis=0)\n",
    "    F=U.dot(C)/m\n",
    "    #print(F.min(),F.max(),F.mean(),l)\n",
    "    temp=np.greater_equal(F, Theta) #porównanie funkcji aktywacji z progiem\n",
    "    for i in np.unique(np.where(temp[:,:]==True)[0]): #interacja po użytkownikach, którzy mają przekroczony próg\n",
    "        temp1=np.where(temp[i,:]==True)[0] #tagi, w których dla użytkownika i przekroczony był próg\n",
    "        #print(i,temp1.shape,l)\n",
    "        temp2=np.where(I[i][temp1]==True)[0] #tagi juz aktywne\n",
    "        temp1=np.setdiff1d(temp1,temp2) #usuniecie juz aktywnych tagow\n",
    "        # CZY NIE TRZEBA OSOBNO OBSLUZYC PUSTYCH temp1?\n",
    "        if not np.any(C[temp1[:, None],temp1]<0): #sprawdzenie, czy kandydaci do aktywacji nie są negatywnie skorelowani\n",
    "            I[i][temp1]=1 #aktywacja uzytkownika i w tagach z listy temp1\n",
    "            Y[i]+=1 #zwiekszenie licznika aktywacji uzytkownika i\n",
    "            Theta[i]=1-(1-init_Theta)**Y[i] #aktualizacja thety\n",
    "        else:\n",
    "            if np.random.rand()<r: #aktywacji pomimo negatywnej korelacji z pr. r\n",
    "                I[i][temp1]=True\n",
    "                Y[i]+=1\n",
    "                Theta[i]=1-(1-init_Theta)**Y[i]\n",
    "    indykatory.append(I)\n",
    "    frakcje.append(np.vstack((range(m),np.sum(I,axis=0)/n)))\n",
    "    I=I.copy()\n",
    "del temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Y[np.ix_([0,3],[0,3])]\n",
    "#plt.plot(frakcje[0][np.ix_([0,1],np.where(frakcje[0]>frakcje[1])[1])][0],frakcje[0][np.ix_([0,1],np.where(frakcje[0]>frakcje[1])[1])][1], 'go')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b75702e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86ed828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86309e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b88b9e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8749a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b51ffe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7e47860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac7a7d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b41732e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7e541d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b89367b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b4086278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86aeeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b4183748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b892ae48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b88e27b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b85d8b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8980a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b81eb3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b87447b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66acb2e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b759dac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b887e940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7e00390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b89a14e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b867d128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7e8cef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b5201b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b82295f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b808c048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac7da748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8895898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b84c07f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b87498d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86f47b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7ae1b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac9cdda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b85de7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8075b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b4055fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b83362e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8857358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66acb48c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8067eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8686da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7ec5d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b833ab38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8673a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8220f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86790b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b84cf550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac7a7198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8925630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86b3860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66acb09da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b88a0898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac7d9b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7e1a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8073e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b80dfa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7eb8b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b881d5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b85b0b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66acb215c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7ea7710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b88871d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b88864a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b82208d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac7da080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7b94e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b81e9a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b5202b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b833aeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b882eb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac799cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8641320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b41837f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7efc2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b5d32390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b406bc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7add128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b51ffac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8815b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b81fb390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b84d75f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86fc3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66acb09f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b80118d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b84cf860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b88b9128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7f89630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b877ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b833a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7b68400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b5d0c358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7fec780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b86798d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b7ec2eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8673dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66ac7de080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3AO9x92/lX0wRERnF0HB397PAjcD9wOPAp939sJntM7N96WJ/BMwAHzezh8xspbASi9RJ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\nP9Nh+VctY9RrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66acaeb7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(N+1):\n",
    "    plt.plot(frakcje[i][1], 'ro')\n",
    "    axes = plt.gca()\n",
    "    axes.set_ylim([0,1])\n",
    "    if i>0:\n",
    "        wzrost=frakcje[i][np.ix_([0,1],np.where(frakcje[i]>frakcje[i-1])[1])]\n",
    "        plt.plot(wzrost[0],wzrost[1], 'go')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "13\n",
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      "18\n",
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      "20\n",
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      "22\n",
      "23\n",
      "24\n",
      "25\n",
      "26\n",
      "27\n",
      "28\n",
      "29\n",
      "30\n",
      "31\n",
      "32\n",
      "33\n",
      "34\n",
      "35\n",
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      "40\n",
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      "96\n",
      "97\n",
      "98\n",
      "99\n"
     ]
    }
   ],
   "source": [
    "for i in range(N):\n",
    "    if np.array_equal(indykatory[i],indykatory[i+1])==True:\n",
    "        print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09407496452331543"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asizeof.asizeof(indykatory)/1024/1024/1024"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAACHUG1kYXQAAAKvBgX//6vcRem9\n",
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       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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JUqOVJFfzw/quWObx/RZXZOY9wJuphge6W64kSZKkkVOSXO1fl7csqv9WXT5w\nmfOurUuXYZckSZI0ckqSq6/X5eIeqtvr8phlzptPuh5U0KYkSZIkNVpJcjXfAzW1qP5KqmF/py5z\n3jPq8s6CNiVJkiSp0UqSq8uokqjHLqq/uC6Pj4jXLHwgIn4ZeC7VQhiXF7QpSZIkSY1WklxdUpcn\nR8S+C+pnga/WP/9RRGyLiI9ExHbg3AXHva6gTUmSJElqtNLk6jNUS6s/eb4yM78BvBC4h6pnaxJ4\nKnBEfR/gtZl5MZIkSZI0Yvbu9oR636rHL/PYByPiscDvACcDhwJ3Uw0F/NvMfMcaYpUkSZKkxuo6\nuVpJZn4BeAFARKzLzF29bkOSJEmSmqZkWOCqmVhJkiRJGhd9Ta4kSZIkaVyYXEmSJElSD5hcSZIk\nSVIPmFxJkiRJUg+YXEmSJElSD5hcSZIkSVIPmFxJkiRJUg+YXEmSJElSD+y93AMRcUr9439m5m0D\nikeSJEmSWqlTz9X7gfcBT1hYGRHn1rcf7mtkkiRJktQiy/ZcdXAOkFTJ1xW9DUeSJEmS2qlTz9V3\n63LfQQQiSZIkSW3WKbn677o8ZhCBSJIkSVKbdRoW+DngZOAVEXEl8Fng7gWPPyAifrCk0cz8asl5\nkiRJktRUnZKrt1IlVw8G3rPosQD+obDNXKFdSZIkSWqdZYcFZuY/Am+hSqQW3uYtru/mJkmSJEkj\npWMPUmaeHRGbgWcDRwI/ADyPqvfpP4Cb+x6hJEmSJLXAisPzMvNS4NL5+xHxvPrHv8jMi/oVmCRJ\nkiS1SafVAiVJkiRJq1SysMRxdXlTLwORJEmSpDbrOrnKzGv6EYgkSZIktVlPlkSPiIOAE4HDgIOA\nbwK3AJdn5jd70YYkSZIkNdmakquIeDrwauDpLL3EekbEh4A/zcyPrqUtSZIkSWqy4gUtIuKvgEuo\nNhpex9L7Wa0Dngl8KCJeu+ZoJUmSJKmhinquIuJPgV9dUHUj8CHgWuAu4EDgGOAZwGR9zK9GxN2Z\n+erycCVJkiSpmbpOriLiR4BXUW0kfCfwcuCfMjOXODaA5wN/CzwQeFVEzGbmFWuKWpIkSZIapmRY\n4Ib6vHuBZ2bm7FKJFUBW/gk4pT5+HXBOabCSJEmS1FQlydWPU/VabcnMudWckJlbgX+kmof14wVt\nSpIkSVKjlSRXR9TlJ7o8b/74wwvalCRJkqRGK0mu5udp3dvlefPH92RvLUmSJElqkpLk6it1+Zgu\nz3v0ovOgw9cUAAAgAElEQVQlSZIkaWSUJFeXUs2d+sWIOHQ1J9THvYRqrtalBW1KkiRJUqOVJFez\ndXkw1ebAD+90cEQ8DPggcEhdtaWgTSLitIi4JiKui4hl98qKiB+LiPsi4mdL2pEkSZKkEl3Pf8rM\niyPiA8CpwA8DV0TEv1AlUNcC3wIOoNpE+JnATwE/QNVr9YHMfF+3bUbEXsDr6ue7Cbg8Ii7KzKuX\nOO5P61gkSZIkaWBKF5d4HnAJ8GNUidPP1belRF1eVp9X4kTgusy8HiAiLgTOAK5edNwrgHfWcUmS\nJEnSwJQMCyQz7wSeCPwBcAdVArXc7Xbg94AnZeY3C+M8HLhxwf2bWLSke0QcDvw08PrCNiRJkiSp\nWPGy6Jl5H/AHEfGnwFOpepcOAw4CvgncStVb9fHM/E4PYl3JXwG/lZm7ImLZgyJiA7ABYHJycgBh\nSZIkSRoHa95zqk6cPlDf+uVm4MgF94+o6xaaBi6sE6tDgWdHxH2Z+Z6FB2XmZmAzwPT0dPYtYkmS\nJEljpS0b+l4OHBMRR1ElVWcBL1h4QGYeNf9zRLwZeO/ixEqSJEmS+qUVyVVm3hcRL6fqHdsLOD8z\nr4qIc+rHzxtqgJIkSZLGXiuSK6iWgAcuXlS3ZFKVmS8eREySJEmSNK9otUBJkiRJ0p5MriRJkiSp\nB0yuJEmSJKkHTK4kSZIkqQdMriRJkiSpB0yuJEmSJKkHTK4kSZIkqQdMriRJkiSpB0yuJEmSJKkH\n9l7LyRHxQ8CpwPHAA4H9VnFaZubpa2lXkiRJkpqmKLmKiMOBNwHP7G04kiRJktROXSdXEXE/4GPA\nw4AoaDMLzpEkSZKkRivpufoN4GiqJOkm4E+BjwA3A3f3LjRJkiRJao+S5OqMurwZOCEzv9bDeCRJ\nkiSplUpWC3wYVa/VuSZWkiQ13OwsrF8P69ZV5ezssCOSpJFV0nN1L7A/cF2PY5EkSb00OwsbNsDO\nndX97dur+wAzM8OLS5JGVEnP1fV1+cBeBiJJknps48bdidW8nTureklSz5UkV2+nWiXQZdglSWqy\nHTu6q5ckrUlJcvU6qiGBz42Ik3scjyRJ6pXJye7qJUlr0nVylZl3Ac8BtgEXRcT/jIiJXgcmSZLW\naNMmmFj0J3pioqqXJPVcySbCF9c/3k61cuCfA5si4irgNmDXCk+RmXl6t+1KkqQuzS9asXFjNRRw\ncrJKrFzMQpL6IjKzuxMidlEtxb5H9RJ1y8rMvbpqtE+mp6dzbm5u2GFIkiRJaqiI2JqZ06s5tmQp\ndqiSqdXULaW7bE6SJEmSWqAkudq/51FIkiRJUst1nVxl5t39CESSJEmS2qxkKXZJkiRJ0iImV5Ik\nSZLUA6ULWuwhIn4IOAk4DDgI+CZwC3BZZl7ZizYkSZIkqcnWlFxFxNnAbwHHdDjm/wF/kplvXktb\nkiRJktRkRcMCI2LfiHg38EaqxCo63I4B3hQR746IfXoStSRJ/TQ7C+vXw7p1VTk7O+yIJEktUNpz\n9UbgjAX3/wP4IHAtcBdwIFVSdQrwpPqYn6zPe1Fhm5Ik9d/sLGzYADt3Vve3b6/uA8zMDC8uSVLj\nRWZ3e/pGxJOAT1BtBnwTMJOZn+xw/BOBLcBUfc5TOx0/SNPT0zk3NzfsMCRJTbJ+fZVQLTY1Bdu2\nDToaSdKQRcTWzJxezbElwwLPrstvAU9bKVHKzP8ATqbq0QL4xYI2JUkajB07uquXJKlWklw9haoH\n6vzMvGE1J2Tm9cD5VHOwnlzQpiRJgzE52V29JA2K80EbryS5OqwuL+vyvPnjH1LQpiRJg7FpE0xM\n7Fk3MVHVS9KwzM8H3b4dMnfPBzXBapSS5Gp+kla350ZBW5IkDdbMDGzeXM2xiqjKzZtdzELScG3c\nuHuhnXk7d1b1aoyS1QJvBY6m2jR4SxfnPW7B+ZIkNdfMjMmUpGZxPmgrlPRcfZyqF+rFEXH0ak6o\nj3sxVa/XJwralNQGjgWXJKk/nA/aCiXJ1T/U5QTw0Yh4SqeD66XbPwwcUFe9qaBNSU23lrHgJmWS\nJHXmfNBW6HqfK4CIeDPwQnbPv7qc3ZsIf4sqkToGeCbV8MF5b83Ms2kI97mSeqh0b6DFG7ZC9cfC\nOS6SJO1pdraaY7VjR9VjtWmTfysHoJt9rkqTq32AtwE/VVd1epL5hSzeDTwvM+/rusE+MbmSemjd\nuqrHarEI2LVr+fPcsFWSJDVYvzcRJjPvzcznUm0ofDVVArXc7WrgRZn5M01KrCT1WOlYcCfoSpKk\nEVGyWuD3ZOZbgLdExCOBE6n2wDoI+CbVqoCXZeY1a45SUvNt2rT08L6VxoJPTi7dc+UEXUmS1DJr\nSq7m1QmUSZQ0zubHfHc7Frw0KZMkSWqYniRXkgSU7Q1UmpRJkiQ1jMmVpOFzw1ZJkjQCiha0kCRJ\nkiTtadmeq4iYnwCRmXnAEvWl9ng+SZIkSRoFnYYF7leXizeu2W/xgV3qfmMtSZIkSWq4TsnVZSyd\nCC1XL0mSJElja9nkKjMf1029JEmSJI0zF7SQJEmSpB4wuZIkSZKkHuh6n6uIOLf+8fWZeUUX5x0H\nvIJqtcCXdduuJEmSJDVZySbC51AtaPF+YNXJFTC54FyTK0mSJEkjxWGBkiRJktQDg0yu5nvJ7htg\nm5IkSZI0EINMrh5el98YYJuSJEmSNBAd51xFxARw4DIPPyAifnCF5w/gAOCxwG9Qzbe6qtsgJUmS\nJKnpVlrQ4jeA312iPoB/KGzznwvPkyRJkqTGWs1qgdFlfSfvBs4rOE+SJEmSGm2l5OpK4G2L6p5H\nNbzvP4CbVzh/F3AXcAPw4cy8vCRISZIkSWq6jslVZr4TeOfCuoh4Xv3jX2TmRf0KTJIkSZLapGQT\n4bdT9Vzd1ONYJEmSJKm1uk6uMvOsfgQiSZIkSW02yH2uJEmSJGlkdZ1cRcQhEfFvEXFxRJy8ynOe\nUR//rxFxv+7DlCRJkqRmK+m5egHwLOCJwKWrPOdTwBOAZwPPL2hTkiRJkhqtJLl6Zl2+LzN3ruaE\n+rh/o9ob67SCNiVJkiSp0UqSq0dTrRa42l6reZ+pyx8paFOSJEmSGq0kufrBuryly/NurcuHFLQp\nSZIkSY1Wklx9ty736fK8+eNdoVCSJEnSyClJdL5Wl4/s8rxj6/K2gjYlSZIkqdFKkqutVAtTnBkR\nsZoTImIdcCbVXK3PFbQpSZIkSY1Wkly9ty4fAfzeKs/53fp4gIsK2pQkSZKkRitJrrYA2+uffyci\n/j4iHrrUgRFxWES8Efgdql6rm4A3lwQqSZIkSU22d7cnZOZ9EfEC4CPAvsAvAi+MiP8EvgDcBRwI\nHAc8tm4jgLuB52fmPT2KXZIkSZIao+vkCiAzL42I04ELgAdRrQR4Yn1baH5O1teAszLzU6WBSpIk\nSVKTFS+Lnpkfoeqd+iPgeqpEavHtS8AfAMdl5kfXEmhEnBYR10TEdRHx6iUen4mIz0fEFRHxqYh4\n9FrakyRJkqRuFPVczcvMO6gWq/jdiHgIcARwP+BO4KbM/PLaQ4SI2At4HfBMqnlbl0fERZl59YLD\nbgCempn/HRHPAjYDJ/WifUmSJElayZqSq4XqRKonydQSTgSuy8zrASLiQuAM4HvJ1aIhh5+mSvQk\nSZIkaSCKhwUO2OHAjQvu31TXLeclwPv6GpEkSZIkLdCznqumiIgfp0qunrTM4xuADQCTk5MDjEyS\nJEnSKOtJchURx7F7vtVeKx2fmW/vsombgSMX3D+irlscx48AbwSelZm3L9P2Zqr5WExPT2eXcUiS\nJEnSkoqTq4g4DPht4AVUSdVqJdBtcnU5cExEHEWVVJ1Vt7swnkngXcAvZOa1XT6/JEmSJK1JUXIV\nEScC7wUOYfdeVn1Tb1z8cuADVD1j52fmVRFxTv34eVSrFh4CnBsRAPdl5nS/Y5MkSZIkKEiuIuJA\n4D3AoezuhfoU8Ff1/TcA1wFTwCnAI+v6C4B/Lw00My8GLl5Ud96Cn18KvLT0+SVJkiRpLUp6rjYA\nD6FKmM7OzLcCRMRf1Y+/PzMvmj84Ip4HnAf8HPBvmXnB2kKWJEmSpOYpWYr99Lr87Hxi1Ulmvg34\nCarhfH8fEccUtClJkiRJjVaSXD2Kqtfq3cs8/n2rBWbmJ4F3ABPAOQVtSpIkSVKjlSRXD6zLHYvq\n76vLA5Y575K6PK2gTUmSJElqtJLk6p663Lmo/s66fOgy532rLg8vaFOSJC1ldhbWr4d166pydnbY\nEUnS2CpJrm6py0MW1d9Ql8stf/6IutynoE1JkrTY7Cxs2ADbt0NmVW7YYIIlSUNSklxdUZfHLqq/\njGrPq9Mj4oiFD0TEQcAvU83V2lbQpiRJWmzjRti5aCDJzp1VvTQs9qZqjJUkVx+nSqKetqh+S13u\nB3wsIs6OiKdExNnA5cBh9eMXIUmS1m7H4unPK9RL/WZvqsZcZGZ3J0RMUQ0BTOBRmfnFBY9dCJxZ\nP/Z9pwI3A4/JzNuLI+6h6enpnJubG3YYkiSVWb+++vC62NQUbNs26Ggkr0mNpIjYmpnLTX3aQ9c9\nV5m5nWrFv+cC31n08IuAWapEavHtSuAZTUmsJElqvU2bYGJiz7qJiapeGgZ7UzXm9i45KTM/uEz9\n3cAvRMQfAicDD6ZaVfBy4GPZbTeZJEla3sxMVW7cWH14nZysEqv5emnQJieX7rmanBx8LNIQFCVX\nK8nMa4Fr+/HckiRpgZkZkyk1x6ZN1RyrhQut2JuqMdL1sMCIOLe+/Y9+BCSpR1ytSZI0aDMzsHlz\nNccqoio3b/YLAI2Nkp6rc6gWrHhVj2OR1CvzqzXNf3M4v1oT+AdOktRf9qZqjJUsxX5HXd7Uy0Ak\n9ZB730iSJA1cSXK1rS4P6WEcUju0ZaidqzVJkiQNXEly9R6qpdVP7XEsUrO1aWPE5VZlcrUmSZKk\nvilJrs4FbgXOiIjn9DgeqbnaNNTOvW8kSU3VllEgUoGSTYTvAH4a+Arwjoj4w4h4SM8jk5qmTUPt\nXK1JktREbRoFIhWIbvf1jYiL6x8fAjyGauXABK4Hbga+vcJTZGae3mWcfTE9PZ1zc3PDDkNtsX79\n0hsjTk3Btm2DjkaSpPbxb6laKCK2Zub0ao4tWYr9NKpkigXlOuDo+iaNJjdGlCRpbdo0CkQqUDLn\nCqoFLRbelqpb7ia1k0PtJI0a575o0FxwSSOupOdq/55HIbWFGyNKGhVuNq5hcBSIRlzJghZ3r/XW\njxciSZK60KYVUDU6HAWiEdf1ghajxAUtJElja926arW2xSJg167BxyNJDdXNghalc64kSVKbOfdF\nknquY3IVEX9Z3x41qIAkSQPiYgbjzc3GJannVuq5+jXglXRYYj0izq9vj+lpZJKk/nEjTzn3RZJ6\nrhfDAl8MvAhwHEGT+I20pE5czEBQJVLbtlVzrLZtM7GSpDUqWYpdTefyupJW4kaekiT1nAtajCK/\nkZa0EhczkCSp50yuRpHfSEtaiYsZtItDvSWpFUyuRpHfSEtaiYsZtIeLj0hSa5hcjSK/kZa0Gi5m\n0A4O9Zak1jC5GkV+Iy1Jo8Oh3pLUGqtdLTB7dIwGZWbGZEqSRsHkZDUUcKl6SVKjrLbn6j0R8d2l\nbvXj0emYRbf7+vRaJGlP/VgEwIUFNGgO9Zak1uhmn6tYpj5XcYwkDVY/9ntzDzkNw/y1tXFjNRRw\ncrJKrLzmJKlxInP50XwRsasPbWZm7tWH5+3a9PR0zs3NDTsMSf2wfv3SQ6mmpqrFG5rynJIkqdEi\nYmtmTq/m2I7DAjNzXR9ujUisxprDmjQO+rEIgAsLSJKkDlwtcNy4X4rGRT/2e3MPOUmS1m6Ev+g3\nuRo37peicdGPRQBcWECSpLUZ8S/6Ta7GjcOaNC76sd+be8hJkrQ2I/5Ff8cFLUbdWC5o4YR8SZIk\nDcu6dVWP1WIRsKsfa+mtXc8WtNAIcljTaBnhMcuSJGkEjfj8ZZOrceOwptEx4mOWJUnSCBrxL/pN\nrsbRzEw1BHDXrqo0sWqnER+zrBFkT6skacS/6HfO1bjNudLoaOGYZY2x+Z7WhV8ITEyM1B9USdJo\ncs6VNA5GfMyyRow9rZKkMWByJbXViI9Z1ohxGwgNi8NRJQ2QyZXUViM+Zlkjxp5WDYML/0gaMOdc\nOedKkvrPOVcaBvd2lNQDzrmSJDWLPa0aBoejShowkytJ0mC4DYQGPf/J4aiSBszkSpIk9d8w5j+5\n8I+kATO5kiRJ/TeM5fgdjippwFzQwgUtJEnqPzc+l9RSLmghSVob9wZSrzn/qeJ7SxppJleSpD25\nN5D6wflPvreayGRXPeawQIcFStKe3BtI/TI7W82x2rGj6rHatGm85j/53moW99/TKnUzLNDkyuRK\nkvbk3BipP3xvNYvJbmXcv/RYBedcSZLKjcvcGIcDadDG5b3VFm4y7VDVPjC5kiTtaRzmxviBQsMw\nDu+tNjHZXdsWCX5BtSSTK0nSnsZhb6Bh7LkkjcN7q01Mdst77/yCalnOuXLOlSSNH+e+SALnG5XO\nOxuz+WrOuZIkqROHA0mCKpHatq36UmXbtvFKrKC89875assyuZIkjR+HA0lS+VBVv6BalsmVJGn8\nOPdFkiolvXd+QbUskyupCVxxRxq8cR8OJEml/IJqWSZX0rCttOKOiZckSf49bBq/oFqSyZU0bJ2W\nhHapUzWRH3AkDZp/D9USJlfSsHVacce9eEbLKCQl9rRKGgb/HqolTK7UbOPwQa3TijsudTo6RuVb\nV3taJQ2Dfw/VEiZX6s4gk51x+aDWacUdlzodHaPyrWs/e1r78ftlHL6gkcZBE/8e+vtFSzC50uoN\nOtkZlQ+jK+m04o5LnY6OUfnWtV89rf34/TIuX9BI46Bpfw/X8vulTUlZm2JtiMjMYccwNNPT0zk3\nNzfsMNpj/frql8diU1PVKjG9tm5d9QtrsYhqZZpxMTtbJZQ7dlQfYDdtckWeNhr0+6df5j9QLPzi\nY2Ki+kJg48by19iPf59R+TeXVGnS38PS3y+dfoc27W97m2Lts4jYmpnTqzrW5MrkatUGnez4wUij\nZJT+SC33AWctr7Efv1/8gqZ/mvQhVxqG0t8vbfps06ZY+6yb5MphgVq9QY93btoQgJWMUtf5KL2W\nphilDReX29tkLa+xH79fmjhHo02W+z3gipFS+e+XlYZP9+v9U/K8ozKcfdAysxU34DTgGuA64NVL\nPB7A39SPfx547ErPecIJJ2SrbdmSOTWVGVGVW7b0v72Jiczqz2l1m5jY3W4/4unXa+z18670b9Mm\no/RaxsGgfw/0Sz+uO6/lcp3+7aam9qyfv81ff+Pybz4q7z11ttz/c+m1Poz3Tz9iHTPAXK42Z1nt\ngcO8AXsBXwIeBuwLfA44ftExzwbeVydZjwM+s9Lztjq5GtYfsF7/khmGfsTaxl9Ay/1ftvG1jIJO\nH9RG4X23GqUfVkv+7dRZp98DEUs/Nv9vPA6/P5r43huVa71Jr6MfXyqXfnGxFqXP27TPmkM0isnV\n44EPLLj/GuA1i455A/D8BfevAQ7r9LytTq6a9gesafF00o9YO33YaKJOvzDb9lpGQaf/j2H8IW6T\nJn7IHQWlCdS4/P5o2ntvVN4HTXsd/fp/Xi556Nf7Zy3P27RRUkPSTXLVigUtIuJngdMy86X1/V8A\nTsrMly845r3An2TmJ+v7HwZ+KzOXXbGi1QtaNG2idtPi6aQfsbZt0meneKFdr2UUlP5/7NjRnvdd\nv7TtvdcWnf5dN23qz4qRbdK0v3mj8j5o2usYlYW8mvbv2klDYx251QJ7mVxFxAZgQ333kVQ9XE1x\nKHDbag78Efjhfaohknu4F+75PFzR88haFk8n/Yj1UDh4EqZiwSIxCbt2wPbb4I61xLv6EFZ37QCc\nACcs99h2uGHIr2XsdPr/6OReuKdH13JX10+TdPq32wpbBxnLKFnpd9qhcPBD4fB9YN974Z5b4Ob5\n+nH4/dG0v3ktfh/s8bunaa9j0P/P/Xr/tOl92cU1MOi/W1OZ+aDVHLh3vyPpkZuBIxfcP6Ku6/YY\nMnMzsLnXAfZCRMytNiuWFvLa0Vp4/aiU147WwutHpZp87bRlKfbLgWMi4qiI2Bc4C7ho0TEXAS+M\nyuOAb2TmrYMOVJIkSdJ4akXPVWbeFxEvBz5AtXLg+Zl5VUScUz9+HnAx1YqB1wE7gbOHFa8kSZKk\n8dOK5AogMy+mSqAW1p234OcEXjbouHqskcMV1QpeO1oLrx+V8trRWnj9qFRjr51WLGghSZIkSU3X\nljlXkiRJktRoJlcNEBGnRcQ1EXFdRLx62PGo2SLiyIj4aERcHRFXRcQr6/qDI+KSiPh/dfnAYceq\nZoqIvSLiv+otLLx2tCoR8YCIeEdEfDEivhARj/fa0WpFxK/Xf7OujIgLImI/rx8tJyLOj4ivRsSV\nC+qWvV4i4jX15+hrIuLU4URdMbkasojYC3gd8CzgeOD5EXH8cKNSw90HvCozjwceB7ysvmZeDXw4\nM48BPlzfl5bySuALC+577Wg1/hp4f2YeCzya6hry2tGKIuJw4FeB6cz8IarFyc7C60fLezNw2qK6\nJa+X+jPQWcCj6nPOrT9fD4XJ1fCdCFyXmddn5j3AhcAZQ45JDZaZt2bmf9Y/f5PqA87hVNfNW+rD\n3gL81HAiVJNFxBHA6cAbF1R77aijiLg/8BTgTQCZeU9mfh2vHa3e3sD+EbE3MAHcgtePlpGZn+D7\nNzhe7no5A7gwM+/OzBuoVg4/cSCBLsHkavgOB25ccP+muk5aUUSsB34U+Azw4AV7u30ZePCQwlKz\n/RXwm8CuBXVeO1rJUcDXgH+oh5S+MSIOwGtHq5CZNwN/AewAbqXai/SDeP2oO8tdL436LG1yJbVU\nRBwIvBP4tcy8c+Fj9dYELgWqPUTEc4CvZubW5Y7x2tEy9gYeC7w+M38U+BaLhnB57Wg59dyYM6iS\n9IcCB0TEzy88xutH3Wjy9WJyNXw3A0cuuH9EXSctKyL2oUqsZjPzXXX1VyLisPrxw4CvDis+NdYT\ngZ+MiG1UQ5CfHhFb8NrRym4CbsrMz9T330GVbHntaDWeAdyQmV/LzHuBdwFPwOtH3VnuemnUZ2mT\nq+G7HDgmIo6KiH2pJuRdNOSY1GAREVTzHr6QmX+54KGLgBfVP78I+JdBx6Zmy8zXZOYRmbme6nfN\nRzLz5/Ha0Qoy88vAjRHxyLrqZOBqvHa0OjuAx0XERP037GSq+cJeP+rGctfLRcBZEfEDEXEUcAxw\n2RDiA9xEuBEi4tlU8yD2As7PzE1DDkkNFhFPAv4duILd82b+N9W8q7cDk8B24MzMXDwZVAIgIp4G\n/K/MfE5EHILXjlYQEY+hWghlX+B64GyqL2m9drSiiPgD4HlUK97+F/BS4EC8frSEiLgAeNr/b+/+\nQ++q6ziOP9/74bDa3MzMRJmlqWsmWqjTzWWGEnMqJrXNQlCJCTGT/lBESyPCciAV4g8SUnChwaI0\nk7LUGFlTtOzHTM3UdDbFpvlbp3v3x7lzZ+d7v3fnzrvv2T3f5wMu3PO5n3M+7/vlC9vr+/mczwF2\nA54BLgZ+xii/LxFxIXAmxe/XuZl5WwNlA4YrSZIkSRoIlwVKkiRJ0gAYriRJkiRpAAxXkiRJkjQA\nhitJkiRJGgDDlSRJkiQNgOFKkiRJkgbAcCVJekdE7BMRuZ1flzT9PZsWEXtUfibrttJ/cY2f65sR\n8WJEPB4RqyPihog4PyLmRcTksfpukjSeTWq6AEmSNBCTO6+pwEzg8NJn6yPiJ8D3MvOhJoqTpPHA\nmStJktpvV+BsYE1EXB0RuzRdkCS1kTNXkqSyp4AP1+x7I3BE6XgJ8Mca573Qb1Ea4RfAskrbBGA6\nMAPYC5gDzAMOqvRZCnw6Ik7IzH+OQa2SNG4YriRJ78jMt4DH6/SNiNcrTesys9a5etdeqfGzvh4g\nIuYC5wMnlj7bH7gjIo7MzLXbp0RJGn9cFihJUotl5u8z8yTgK8CbpY/2BlZERDRTmSS1j+FKkqRx\nIDOvpLjvquxTwGkNlCNJreSyQEnSDiEiJgKzOq8PUex69yqwHlgD3J+Zbw9gnL2BucCenaangAfG\nwy56mfmjiDgeWFxqvgBY0VBJktQqhitJUmMiYipwCnAqxSxKr13sXoqI64DLMvOpbRjrk8DlwNHA\niKVwEXE38I3M/G3n+HVgSufjmzJzcfWcIfUttgxXsyNiTmbW2YxEktSDywIlSU1aSbHxwkn0DlZQ\nzGQtA/4aEZ/tZ5CIWAasBubTJVh1HAX8OiLO7+fawyYz1wB3VZoXNFCKJLWOM1eSpCZV/8j3LMUS\nwPXAaxSBaxawb6nPdODmiJibmfdubYCI+DLwg0pzAvcBjwE7AQcCB3Tq+U5EPNr/VxkqdwDHlI6P\naqgOSWoVw5UkqWmrgRuAWzLziW4dImIW8E3g852myRQ73c3qdR9WROwLfL/SfAuwrDpWRBwGXAMc\nClxLu/+NXF05/ngjVUhSy7gsUJLUpLMyc05mXjFasALIzAcz8wvA8lLzRymWE/ZyGbBz6XgFcHK3\nsTqzYPOBeylmzCbW/A7DqLp5x+4RMaVrT0lSbYYrSVJjegWqUVwIlM9ZNFrHiNiTLcPX08DZmZk9\n6nkZOB3Y0Gddw+aFLm3vH/MqJKllDFeSpKGRmRuAX5aajujR/RS2XNp3ZSc8bW2MfwA3b1uFQ+NF\nYGOlbeduHSVJ9bV5PbkkaUhFxCRgGvA+Rv4h8NXS+30iYkpmvtHlMnMqxyv7KGElxfbwbRWMvmui\nJGkbGa4kSY2LiBkUm1UsBA4GZvZx+gxgXZf2g0vvXwEe7uOa9/fRdxhNY2S4eq2JQiSpTQxXkqTG\nREQAX6XYCXDaNl5mGt3DVfkeorWZWV0G18uT21jLsJheOU7guSYKkaQ2MVxJkpp0FbD0XV5jtPuH\nyxeoCv8AAAQbSURBVA8lfqmfC2bmqxHxNu3dMfDAyvGzmflmI5VIUou4oYUkqRERsYiRweoO4ByK\nh9ruDUwFJmVmbHoBF9QcohwWJvdZ20TaG6xg5EYgf2mkCklqGWeuJElN+XrpfQJLMvOmGudNrXn9\n54FdO+9n9FPYNvQfNsdWjv/QSBWS1DLOXEmSxlxEzARml5pW1AxWAHvU7Pfv0vu9IqKfe7pmb73L\ncIqIgygellx2axO1SFLbGK4kSU3Yr3L8qz7OrW6xPpp7Su+DkYGil376DpuLKsd/z8x7uvaUJPXF\ncCVJasIuleMX65wUEYcAH6s5xp2V4zNqjjEROL3mGEMlIs4EFlWaL22iFklqI8OVJKkJL1SO9695\n3rf7GON2tlwa+LmIOKbGeecwcmZt6EXE2RS7M5b9DvhxA+VIUisZriRJTfgbxSYWmyyNiPf0OiEi\nLgYW1B2g81yr71aaV0bEYT3GWARcVneMYRARR0XEzymC1U6lj54ETsvM7H6mJKlf7hYoSRpzmfls\nRKxi871N+wG3RcQZmfmvct/O5heXAks6Tc8Bu9Uc6mrgNGBu53hX4O6IuB74KfAYxTbts4AvAQs7\n/W4Bjgem9PnVxsp7I2KfStsEiuWW04G9KO5Nmw8c1OX8h4ETMvPp7VijJI07hitJUlMuorgvatPz\npOYDj0TEfcCjFKHnI8AhFBtSANxHEXwuqTNAZm6MiFOBu9j84NxJwFmdVzdPUNyftbZ8qTrjjaGF\nbA6C/dgIXAucl5n/G2xJkiSXBUqSGpGZq4BlFP/h32QCcBiwGDgVOJQtg9UC4I0+x3kGOAa4uUb3\nO4HDKZ6RVV5C93I/Y+6A1gPXALMzc6nBSpK2D2euJEmNycyrIuIhYDnwiVG6PQb8ELg8M9+IiFG6\n9RznGeDkiDgW+CIwD9iTYkZqLfBn4Drg9s5s1ww2hzqAYQgjb1EEz/XAOuARinvbVgGrM3NDg7VJ\n0rgQ3scqSdoRRMQs4AjggxRB4T/AI5l5bwO1HAncXWo6LzOXj3UdkqTh4syVJGmHkJkPAg82XUfH\nvMrxnxqpQpI0VJy5kiSpJCImAGuAAzpNG4HdMvP55qqSJA0DN7SQJGlLX2NzsAK4zWAlSarDcCVJ\narWI+ExELI+ID2yl34SIOJeRDx6+YvtVJ0lqE5cFSpJaLSIWUjwbawNwK/Ab4AGKhxEHsDtwJMVD\nhGdXTr8xM5cgSVINhitJUquVwlW/VgEn+kwoSVJdLguUJLXdSxSzVnW9BlwOHGewkiT1w5krSVLr\ndR4KvAA4GjgYmAnMAHaiCF//pXjg7p3ATZm5rqFSJUlDzHAlSZIkSQPgskBJkiRJGgDDlSRJkiQN\ngOFKkiRJkgbAcCVJkiRJA2C4kiRJkqQBMFxJkiRJ0gD8HzIEmzktFlBXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b870a7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "   # plt.plot(frakcje[i][1], 'ro')\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_ylim([0,1])\n",
    "fig.set_size_inches(14, 8, True)\n",
    "ax.set_xlabel('Tag ID', fontsize=40)\n",
    "ax.set_ylabel('Fraction of active users', fontsize=30)\n",
    "\n",
    "x = np.arange(0,m)\n",
    "line, = plt.plot(frakcje[0][1], 'ro')\n",
    "\n",
    "\n",
    "def animate(i):\n",
    "    line.set_ydata(frakcje[i][1])  # update the data\n",
    "    return line,\n",
    "\n",
    "\n",
    "# Init only required for blitting to give a clean slate.\n",
    "def init():\n",
    "    line.set_ydata(np.ma.array(x, mask=True))\n",
    "    return line,\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, np.arange(1, m), init_func=init,\n",
    "                              interval=70, blit=True)\n",
    "\n",
    "#dpi = 300\n",
    "#writer = animation.writers['ffmpeg'](fps=30)\n",
    "#anim.save('power_law.mp4',writer=writer,dpi=dpi)\n",
    "\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.00527645],\n",
       "       [-0.00527645,  1.        ]])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(cor_23_45, rowvar=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000000, 2)"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cor_23_45.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.02579039],\n",
       "       [-0.02579039,  1.        ]])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(cor_23_45.reshape((n,2*N))[:,[2,3]], rowvar=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.6/site-packages/numpy/lib/function_base.py:3003: RuntimeWarning: invalid value encountered in true_divide\n",
      "  c /= stddev[:, None]\n",
      "/opt/conda/lib/python3.6/site-packages/numpy/lib/function_base.py:3004: RuntimeWarning: invalid value encountered in true_divide\n",
      "  c /= stddev[None, :]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.61068905277670815"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Npap45LWj+OGLNVg4rRCb7lyRtNU3f9x3Gj98sQZzp0zAmoVTce3CqbZq6FDE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f66b8663da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp=[]\n",
    "for i in range(int(N/2)):\n",
    "    tmp.append(np.corrcoef(cor_23_45.reshape((n,2*N))[:,[2*i,2*i+1]], rowvar=False)[0][1])\n",
    "plt.plot(tmp)\n",
    "C[23][45]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
